Final answer:
The answer is False; displacement does not depend on the path taken but only on the initial and final positions. Additionally, waves of different frequencies can superimpose, and the graph of an object speeding up will show a curve, not a straight line.
Step-by-step explanation:
Displacement Comparison Between Two Paths
Regarding the statement about the displacement of two people walking different paths, the correct answer is False. Displacement is a vector quantity that depends only on the initial and final positions, not on the path taken. Whether a person walks 2 blocks east and 5 blocks north, or 5 blocks north and then 2 blocks east, the resulting displacement is identical because both individuals start and end at the same points. Thus, their displacements are the same, and comparing the magnitude of these displacements would show no difference.
When it comes to waves, the statement that waves can superimpose if their frequencies are different is True. Superposition of waves occurs when two or more waves travel through the same medium simultaneously. The waves pass through each other without being disturbed by each other's presence, which can occur regardless of whether they have the same frequency or different frequencies.
The position vs time graph of an object that is speeding up will not be a straight line but rather a curve that gets steeper over time. So, this statement is False. The steeper the slope of the curve, the faster the object is moving. If acceleration is constant, the graph will be a parabolic curve.